数学竞赛不等式一题多解的数学教育价值  

Mathematics Education Value of Multiple Solutions to Mathematics Competition Inequality

作　　者：张传军 张东方 侯先融 ZHANG Chuan-jun;ZHANG Dong-fang;HOU Xian-rong(Refueling Science Research Institute,Guizhou Normal University,Guiyang,Guizhou,5550001;Guangzhou Binjiang No.5 Middle School,Guangzhou,Guangdong,510006;School of Mathematics and Statistics,Qiannan Normal University for Nationalities,Duyun,Guizhou,558000)

机构地区：[1]贵州师范学院教育科学研究所,贵州贵阳550001 [2]广州市滨江五中学校,广东广州510006 [3]黔南民族师范学院数学与统计学院,贵州都匀558000

出　　处：《贵州师范学院学报》2022年第12期59-64,共6页Journal of Guizhou Education University

基　　金：2022年贵州省理论创新课题贵州师范学院联合项目(重点专项)“贵州省普通高中新课程实施的策略研究”(GZLCLHZXZD-2022-05);2020年贵州省教育厅基地项目“贵州乡村小学布局调整研究”(2021JD040)。

摘　　要：数学竞赛是中学数学教育中的一个重要组成部分,同时也是一个提升学生数学思维和数学能力的重要平台。数学竞赛的难度一般高于教材,具有一定的挑战性,但考查内容仍基于中学数学内容,更注重数学知识的综合运用,重视运用数学思想方法解决问题,解题方法上具有很高的技巧性。以2019年全国高中数学联赛的一道试题为切入点,探究此类试题对学生数学能力和思维培育的影响。通过分析发现此类试题在培养学生的数学抽象、数学运算、逻辑推理等核心素养以及发展学生的发散思维、理性思维方面具有重要作用,对数学教育质量提高具有重要意义。Mathematics competition is not only an important part of mathematics education in middle schools,but also an important platform to improve students′mathematical thinking and ability.Mathematics competition,generally more difficult than textbooks,with a certain challenge,mainly examines students′knowledge of middle school mathematics,pays more attention to comprehensive application of mathematical knowledge,attaches importance to the use of mathematical thinking method to solve problems,and values high skills in solving methods.In this paper,a test question from the national High School Mathematics League in 2019 is taken as the entry point to explore the influence of such questions on the cultivation of students′mathematical ability and thinking.It is found that these questions play an import role in cultivating students′core qualities such as mathematical abstraction,mathematical operation and logical reasoning as well as developing students′divergent thinking and rational thinking.

关 键 词：不等式 一题多解 数学教育 均值不等式 

分 类 号：G633.62[文化科学—教育学]